{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('../transformers/')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import tensorflow_datasets as tfds\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import pickle\n",
    "from tqdm import tqdm\n",
    "\n",
    "from path_explain import utils\n",
    "from plot.text import text_plot, matrix_interaction_plot, bar_interaction_plot\n",
    "from model import cnn_model\n",
    "\n",
    "from embedding_explainer import EmbeddingExplainerTF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "utils.set_up_environment(visible_devices='3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "encoder = tfds.features.text.TokenTextEncoder.load_from_file('encoder')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = tf.keras.models.load_model('model.h5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "interpret_model = cnn_model(encoder.vocab_size, for_interpretation=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "interpret_model.load_weights('model.h5', by_name=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "sentences = [\n",
    "    'This movie was bad',\n",
    "    'This movie was not bad',\n",
    "    'A movie',\n",
    "    'A bad movie',\n",
    "    'A bad, terrible movie',\n",
    "    'A bad, terrible, awful movie',\n",
    "    'A bad, terrible, awful, horrible movie'\n",
    "]\n",
    "\n",
    "ids_list = []\n",
    "for sentence in sentences:\n",
    "    ids = encoder.encode(sentence)\n",
    "    ids = np.array(ids)\n",
    "    ids = np.pad(ids, pad_width=(0, max(0, 52 - len(ids))))\n",
    "    ids_list.append(ids)\n",
    "ids_list = np.stack(ids_list, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(7, 1), dtype=float32, numpy=\n",
       "array([[0.05548102],\n",
       "       [0.02436904],\n",
       "       [0.54755235],\n",
       "       [0.02286368],\n",
       "       [0.00701833],\n",
       "       [0.00253859],\n",
       "       [0.00068946]], dtype=float32)>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(ids_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "embedding_model = tf.keras.models.Model(model.input, model.layers[1].output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "embeddings = embedding_model(ids_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "baseline_embedding = embedding_model(np.zeros((1, 52), dtype=np.float32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "explainer = EmbeddingExplainerTF(interpret_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 7/7 [00:00<00:00, 16.78it/s]\n"
     ]
    }
   ],
   "source": [
    "attributions = explainer.attributions(inputs=embeddings,\n",
    "                                      baseline=baseline_embedding,\n",
    "                                      batch_size=128,\n",
    "                                      num_samples=256,\n",
    "                                      use_expectation=False,\n",
    "                                      output_indices=0,\n",
    "                                      verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 7/7 [00:17<00:00,  2.43s/it]\n"
     ]
    }
   ],
   "source": [
    "interactions = explainer.interactions(inputs=embeddings,\n",
    "                                      baseline=baseline_embedding,\n",
    "                                      batch_size=128,\n",
    "                                      num_samples=256,\n",
    "                                      use_expectation=False,\n",
    "                                      output_indices=0,\n",
    "                                      verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['UNK', 'movie', 'was', 'not', 'bad']"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "encoder.decode(ids_list[i]).split(' ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "i = 1\n",
    "text_plot('this movie was not bad'.split(' '), attributions[i], include_legend=True)\n",
    "plt.savefig('movie_not_bad_cnn_text.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "i = 1\n",
    "matrix_interaction_plot(interactions[i, ids_list[i] != 0][:, :5], encoder.decode(ids_list[i]).split(' '))\n",
    "plt.savefig('not_bad_cnn_matrix.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_all(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_all(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOkAAAAgCAYAAAD30F+fAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAM8ElEQVR4nO2cf1SUVf7HX4M4rA5pAgIq4uAooWGi8g0DI3AQUETRVVCJmDUVy5QNf2AIAgErm4qrkUeLHHUiWM6iKOsRCvyRv6Aw93zdzPIHoqUgyJYsP2QQ949glsEBRgWD7XmdM2fOfZ77+Tzve+d+nvu595kZ0YMHDxAQEOi+GPzaAgQEBNpHCFIBgW6OYdN7KWDxawp5AsoAyx9OneppbSizcnGxrC4r62m6nzZlEgsLS3r2GH0Syppn0p7ceItW7z2Fnqr7afNb7ycLId0VEOjmCEEqINDNEYJUQKCbIwSpgEA3RwhSAYFujl5BqlAosLKy0nnu2LFjiEQi8vLyAHBzc0MkEvHaa689VDclJQWRSMS1a9c69P3RRx9hYGCAQqHg/v37+shsl6SPP2bopEk0NDQ8sa+2eDshgZfmzOlUn9mHD/P+jh2d6rMjRjs6ErJihab8SXo6xpaWXCkubteu5Pp1jC0t+SQ9vasldlsUCgVSqbRTfXbZTJqamsqFCxceyzY5OZmQkBCWLFmCUqmkV69enayu5/D3w4d5f+fOp3rNNKWS8LCwp3rN/xWioqLYv39/p/rskiB1cHDAzMyMqKioR7bdtGkTy5cvZ/ny5ezYsQORSNQFCn+73Lt3r8NzY8eMYXgnzwa/FWQyGePGjetUn10SpBKJhIiICPbt28fZs2f1touPj2f16tWsWbOGrVu3doU0LpWU4L98OSPlcibMnMmmlBQaGxsBqLt3j5ht25AHBfHclCmMnzGDP6xZw+WSkof8nCwqYurChYyYPBkXf38+ycrqdK0hK1aQmpHBzVu3MLa0xNjSktGOjgCUV1SwYs0aRjo4YGJtzbhJk9ilUmnZN6epJ8+c4dVFixhia4vbtGka37bjxlFYVIR8+nTMpFIi4+KAh9PdZm6VljJPocBi+HCsR43i7bVrqa2t7bAdJ06fxmfOHCxlMsxtbJg5bx7ffPvtk3aPFjExMYhEIi5evIiXlxcSiQRra2uUSiUAKpUKOzs7jI2NcXd358qVKxpbtVpNZGQkUqkUsViMVColMjIStVoN/HLzMjExIUxHdpGRkYFIJOLcuXOA7nS3pqaG8PBwbGxsEIvF2NjYkJCQoBl3HWHYcZXHY+nSpSQlJbFu3TpycnI6rB8VFUV8fDzr168nNja2q2Sx6J13CPDxYVlQEMcLC9m6ezcGIhFhr79OvVpNdU0NK4KDMTc15ae7d1Ht349fSAhHUlMxNzUF4NK1awSvXs0LdnYkx8RQr1azZdcuqmtr6WXQefe98LAwKu7c4ew//kHG3r0AGInF3K2qwnPmTGrr6ohYtQqptTV5R4/yx/Bw7t27xxuLFmn5eX3ZMub6+fFJSorWmvzu3bsoQkJY8cYbRL/zDn369Gm/7956i9m+vixWKCg6d47EpCRqamrYuW1bmzY5n39OgEKBt4cHKR98AMCW5GS8/PwoOHIEqyFDHrd7dDJ37lwWL17MqlWr2L59OwsXLuTSpUscO3aMxMRE1Go1oaGhLFiwgMLCQgCCg4PJyMggIiKCSZMmcfr0aRISErh69SqffvopRkZG+Pv7k5aWxsaNG7WWXyqVCnt7+zZnz4aGBry8vLhw4QJRUVGMGTOGgoIC4uLiqKysZPPmzR22qcuC1MjIiPXr17No0SJOnDjByy+/3GbdH3/8kfj4eIKCgro0QAEW+PqyLCgIgFdefJF/19TwYXo6r/v70/+ZZ9i4dq2m7v3793FzcmKcry8H8vJYHBAAwLY9e5D07UtqUhJ9mwa2o709kwICsDAz6zStw6VSzExNEYvFvDhhguZ4YlIS13/4gcKjRxkxfDgA7q6u/Hz3LhuSklisUGBo+N+P1m/6dOLXr3/I/7+rq0n54AOme3vrpcdTLudPMTEAyJs2COPfe49VoaGMlMl02qyJimLSSy/x1z17NMdcXVywd3Ji244dvNc0e3cWq1ev1mxaOjo6kp2dzc6dOykuLqZfv34A3Lp1i9DQUEpKSqiqqiItLY3o6Ghimtrm6emJoaEhUVFRrF27lhdeeIGgoCB27txJXl4eXl5eAJSXl5OTk0NCQkKbetLS0jh58iTHjx/H1dUVALlcDkBsbCzh4eGYm5u326YufQSjUCiwtbUlIiKi3XpmZmY4OTmRkZFBbm5uV0pi+uTJWuUZcjnVtbV8d/UqANn5+fguXszz3t5IX3kFWw8PqmtruXr9usbm63/+k8kTJ2oCFGCwhQWOY8Z0qfZm8o4exXHcOKTW1jQ0NGhecjc3Kisrufj991r1fadO1emnd+/eTJ0yRe/rzp4xQ6s8x8+PxsZGzjaleq25fPUqV69dI2D2bC2dffv0wWnCBE4VFOh9bX2Z2qKtAwYMwNzcnIkTJ2oCFMDOzg6AGzdu8MUXXwDw6quvavlpLh8/fhwAFxcXZDIZqhZLivT0dBobGwkMDGxTT05ODsOGDcPZ2VmrDzw9PVGr1RTo0Qd6zaSGhoZtPgZpPt7yzt1Mr169ePfdd5k3bx6HDx9u07+RkRE5OTnI5XJmzZrFoUOHcHd310faIzPQxESrbNZULq2o4POTJ3kzOpo5U6fy9sKFDOjfHwMDA4JXraKuvl5jU3bnjsauta8bt251ie6WlFdUcKW4mGfbeCx2p7JSq2xpofu76Wampo+0c27eKkswHzgQgJtttLm8ogKAN8PCeFPHem5oJ6e68EtgtkQsFus8BlBXV0dlU18NGjRIq46lpSWA5jz8EribNm2iuroaiUSCSqVi8uTJDGmnHbdv36akpITevXvrPH/nzp0O26RXkJqbm1NRUUF9fb2mgc3cvHkTAIs2BoK/vz+JiYlERkaydOnSNq/x7LPP8tlnn+Hu7o6vry+5ubm4uLjoI++RKK+sZFiLTq1o+hAszcxQZWUhtbJiy7p1mvPqhgZ+qqrS8mFhaqqxa4muY12ByYABDDQzazNVHDlihFa5rR3yR905v11RweiW5fJyAAa3GuAtdQLErluHu47lTuux9Gtg0nyTLi1F1iJlLy0t1ToPaJZj+/btw8nJia+++oo9LdJ4XZiammJjY0NGRobO8/o8U9Ur3XV3d6ehoYGDBw8+dC4zM5NBgwbx3HPP6bQViUTEx8fz9ddfk5mZ2e51TE1NycvLw9rammnTpvHll1/qI++R+PuRI1rlg/n5SPr0wU4mo7auDsNWM0tmTs5DWcR4e3uOFBRQ02Jn82ZZGUXnz3e6XrGREXV1dVrHPNzd+f7yZayGDGG8g8NDr2eMjTtdB8C+Vp//37KyMDAwwHH8eJ31bUeMYNjQoXz73Xc6ddqPHq3T7mnSvE5Mb/UFjNTUVOCXL+c0I5PJcHZ2RqVSoVKpkEgkzJ49u13/3t7e3LhxA2NjYxwdHR96memxh6HXTOrh4cGUKVNQKBRcvHgRJycnqqqqSE9P58CBAyiVSgza2dX08fHBxcVFr/Wmubk5+fn5uLq64u3tTX5+fqc+d/o0O5vGBw8YO2oUxwsLScvOJmzhQvoZG+Pm5ETuiRPEbNuGh7Mz/3/xIsrMTPq3GvQrgoM5dPQogWFhhMyfj1qtZotSqTMFflLsbG1R/utffLR7N+PHjsXod7/jrZAQMg8exMvPj2VLljBSJqOmpobvL1/mdGGh1iZNZ/JZfj7rYmORu7lRdO4cGzZvZsHcuZrNq9aIRCKSNmwgQKGgvr6e2TNmYGpiwu3ycgqLihg6ZAjL28mungb29vbMnz+fmJgYGhoacHZ25syZM8TFxTF//nzGtNpnCAoKYtmyZZw/f55Zs2Zh3MENMTAwEKVSiVwuZ+XKlYwdO5b6+nquXLnCwYMHycrKom/fvu360CtIRSIRBw4cICEhgb179xIXF4dYLMbBwYGsrCxmzpzZoY+EhAStu1J7DBo0iCNHjuDq6oqnpyfHjh3j+eef18u2Iz5OTGT9li1s3b2bfsbGrAgOJlShAGDBjBncvH2bvx46ROqBA4wdNQrln//M4lYbXyOlUvZs3EjC9u0si47G0syMNwIDOfvNNxS0sYnyuCgWLOCrs2eJ3bCBn37+GWsrKy4UFZGfnU1iUhJbkpO5WVpK/379GDliBH4+Pp16/ZakJCfz/o4dpOzZg1gsRhEYyJ+io9u18fLwIDcri41/+QtvrVxJbV0dFgMH8n8TJvB7PcbN02D37t0MHz6cXbt2ER8fz+DBgwkPDydaR9sCAgIIDQ2ltLSUoKanBO3Ru3dvcnNzSUxM5MMPP6S4uBiJRIJMJsPHx0evlF/U9G+BPf0vA0U/nDrV49pg5eIiqi4r63G6nzYSCwsRPX+MPjbCr2AEBLo5QpAKCHRzhCAVEOjmCEEqINDNEYJUQKCbIwSpgEA3RwhSAYFujhCkAgLdnOYgLftVVTwZZa3eewo9VffT5rfeT2X/AUWqeZPEXbzmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WLfkkLY327doxdORIvj19uj7mPRZZ1W66HxQKpICFjg4KlUpjQE6XlFBdmq11dflVqURRScjvl5VxpQFeSqqOVE+Ph9VOvvh5enLhyhWsLC3p5uio8TEyNGxwOwDSP6u6Ibb3009p1qwZL3TtqjW/vY0N7du25dzFi1rtdHj++Qazrbi4GEm1SWHTpk0a+WQyGa6uriQnJ/Pzzz+rV9x9+vTh2LFjHD16tN6uFGtra85WcyUdOHDgT/agYXH39uKHr7/l+pX/vVhXWlrK/pRUHLu5VFmFNyQHdu2uEt63MxVDIyM6dXXUmv8FD3eMWrTgysWLOHd/QeNj16nhrpE/S4VbbsfOnVXiPy7fR/Hx8VHH2dnZ4enhQWJSEolJSRgaGjLspZdqrb9/v35cu3YNIyMj3NzcND6taniSrqBeK3F/X1/8/fx47Z//5Nxvv9HDzY3CggJSdu9m3yefsHb1apo1q3k+COzfH49everl727TujUH09LoGxTE4Jdf5mBaGt1cXOpjZr34uqQEFdBeR4dzSiXflJQQUL6p2UlXl58ePiT9wQO6SCRcLy3lC7mc6g85/lIpP5aUsLaoCF+plFKVis/kcowacFOzgudtbbmXl8fmnTtxcXCguVTKpNBQ0j/7jKHjxzMxNBQ7GxuKHzzgwuXLfH3mTJVNxIbk6MmTLFixAl8PD86cPcvyNWsYMWiQenO1OoIgsDgykrDp01GUlDC4Xz9aymTcunOH77KysLK0ZHKlEwB/hQEDBrBlyxacnJywt7dn9+7dfPnll1rz+vn5sXTpUtq0aYOj4yNx8fX15c6dO9y+fZu3Kp3gqY3g4GBiYmKIjY2lV69enDhxosoG6dPk1alvkLo1kTFBg5kWNRcj4xYkrlnH5fMX2JiW2mjtJm/cTFlZGc5u3Tl++Ag7Nm5mWtQcjE1MtOZvYWxM5HsxRE+N4O7t2/j074exiTE5f2Tz9YkT9PL2ZsiokY1mb33o2rUrwcHBLFi4EKVSiYeHB6dOnSImNpbg4GCcnJyq5A8JCeHNqVM5e/YsQ4cMwaiOp4mQ0aPZsmULAf37EzFtGs4uLigUCi5dvEj6/v3sSU3FoJJ3oDr1EnFBENj18ce8t3w5ScnJLF66FD09PZydnEhJSuIfAwfWWceCefPoN2hQfZrD0sKCT9PT6RsUxKBhw/hs/34cumg+av0ZxhsYsPfBA47I5TQXBPylUvqWnzpx19MjT6XiW4WCUwoF7XV0GG9oyJaioip1mOvoEG5oyIEHD0gsLsZEEPCVSrlaWsqlBj5mOHrYME7/5z8sTkggr6CAdpaWfHfwIPu2bGHFmjWs2rSJnJs3MW7RAnsbGwb6+zdo+5VZFRvLR9u2sSUlBT2JhJBhw3i3/LRKTfTt3Zu9GzYQv349MxYs4KFcTmszM7o7OzOkf/9ayz4OCQkJqFQq5s6dC0BQUBDbt2+nZ0/Nl1IqRLzyirvi5MqPP/5Y75V4ZGQk9+/fZ9WqVbz33nsEBQWxbds23LW4jp405m0t2Zl5mCVzool6cxpyuRwHF2c2pqXi0z+g0dpduyuZ+dNnkhC3hBYmxrwROZs3575Ta5nRr72KZbt2rF0RT3pyCkqlEgurtvR40RMHF6dayz4pNm3YgG2HDmzavJnYuDjatm3L7FmziNZy3PSVkSOZHhFBTk4OoeXvZdSGRCLh4CefsOT991m3YQOXL1/G0NAQO1tbgoKCNFzY1RFUKhXyvLwm/S/vpSYmwjKZrMn1Yeb9+0JuVlaTs/tJY+7iIgDPwjgJAFdKip6FvjYYNhJDAaBMqXwmx038K4YiIiIiTRhRxEVERESaMKKIi4iIiDRhRBEXERERacKIIi4iIiLShBFFXERERKQJI4q4iIiISBNGFHERERGRJkyFiGv+pZymQ261n02Fpmr3k+ZZGafcGn4XqZ1nftz+C2jY+Gp29MDNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 7.2x7.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(6)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
